46 Mr. 0. Heaviside on MaxwelFs Electromagnetic 



that is when t = CZIv, t]ie curve is A 1 1 1 1 Z f there be no 

 Jcvkage, when R and L are such that e-^* =i. At the 



origin V=^Vo, 



back 



at the front 



V — 4 V o- 



Now introduce leakage to make R/L = K/S. Then 

 2 2 2 2 1 Z shows the curve of V, provided e~^'/^ =^. We 

 have V = ^Vo on the left, and V = jVo in the rest. 



Thirdly, let the leakage be in excess. Then, when Vq has 

 fallen, by leakage only, to ^Vq on the left, the curve 3 3 3 3 1 Z 

 shows V ; it is jqVo at the origin, — §-Vo at the back, and 

 :^Yo at the front. 



Of course there has to be an adjustment of constants to 



make e '^^ ^^ be the same ^ in all cases, viz. the attenua- 

 tion at the front. 



18. Precisely the same applies when it is Cq that is initially 

 given instead of Vq, provided we change the sign of or. That 

 is, we have the curve 1 when the leakage is in excess, and the 

 curve 3 when the leakage is smaller than that required to 

 produce nondistortional transmission. 



19. Now transferring attention to the general medium, if 

 we make the substitution of magnetic conductivity for the 

 resistance of the wires, the curve 1 would apply when it is Eg 

 that is the initial state and g in excess, and 3 when it is defi- 

 cient ; whilst if Hq is the initial state, 1 applies when g is 

 deficient, and 3 when in excess. But g is really zero, so we 

 have the curve 1 for that of H and 3 for that of E. 



Tliis forcibly illustrates the fact that the diffusion of charge 

 in a submarine cable and the difi'usion of magnetic disturb- 

 ances in a good conductor, though mathematically analogous, 

 are physically quite different. They are both extreme cases 

 of the same theory ; but they arise by going to opposite ex- 

 tremities ; with the peculiar result that, whereas the time- 

 constant of retardation in a submarine cable is proportional to 

 the resistance of the wire, that in the wire itself is proportional 

 to its conductivity. 



20. Going back to the diagram, if we shift the curves bodily 



